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Characterization of Efficient Influence Function for Off-Policy Evaluation Under Optimal Policies

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  • Haoyu Wei

Abstract

Off-policy evaluation (OPE) provides a powerful framework for estimating the value of a counterfactual policy using observational data, without the need for additional experimentation. Despite recent progress in robust and efficient OPE across various settings, rigorous efficiency analysis of OPE under an estimated optimal policy remains limited. In this paper, we establish a concise characterization of the efficient influence function (EIF) for the value function under optimal policy within canonical Markov decision process models. Specifically, we provide the sufficient conditions for the existence of the EIF and characterize its expression. We also give the conditions under which the EIF does not exist.

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  • Haoyu Wei, 2025. "Characterization of Efficient Influence Function for Off-Policy Evaluation Under Optimal Policies," Papers 2505.13809, arXiv.org, revised Jun 2025.
    • Handle: RePEc:arx:papers:2505.13809
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    References listed on IDEAS

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    1. Chengchun Shi & Jin Zhu & Shen Ye & Shikai Luo & Hongtu Zhu & Rui Song, 2024. "Off-Policy Confidence Interval Estimation with Confounded Markov Decision Process," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(545), pages 273-284, January.
    2. Bian, Zeyu & Shi, Chengchun & Qi, Zhengling & Wang, Lan, 2024. "Off-policy evaluation in doubly inhomogeneous environments," LSE Research Online Documents on Economics 124630, London School of Economics and Political Science, LSE Library.
    3. Chengchun Shi & Zhengling Qi & Jianing Wang & Fan Zhou, 2024. "Value Enhancement of Reinforcement Learning via Efficient and Robust Trust Region Optimization," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(547), pages 2011-2025, July.
    4. Luo, Shikai & Yang, Ying & Shi, Chengchun & Yao, Fang & Ye, Jieping & Zhu, Hongtu, 2024. "Policy evaluation for temporal and/or spatial dependent experiments," LSE Research Online Documents on Economics 122741, London School of Economics and Political Science, LSE Library.
    5. Susan Athey & Stefan Wager, 2021. "Policy Learning With Observational Data," Econometrica, Econometric Society, vol. 89(1), pages 133-161, January.
    6. Shi, Chengchun & Zhang, Shengxing & Lu, Wenbin & Song, Rui, 2022. "Statistical inference of the value function for reinforcement learning in infinite-horizon settings," LSE Research Online Documents on Economics 110882, London School of Economics and Political Science, LSE Library.
    7. Chengchun Shi & Sheng Zhang & Wenbin Lu & Rui Song, 2022. "Statistical inference of the value function for reinforcement learning in infinite‐horizon settings," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 765-793, July.
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